Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2019, , 222 - 235, 01.02.2019
https://doi.org/10.31801/cfsuasmas.443735

Öz

Kaynakça

  • Abbassi, M., T., K., Note on the classification theorems of g-natural metrics on the tangent bundle of a Riemannian manifold (M; g), Comment. Math. Univ. Carolin. 45(2004), 591-596.
  • Abbassi, M., T., K., Sarih, M., On some hereditary properties of Riemannian g-natural metrics on tangent bundles of Riemannian manifolds, Differential Geom. Appl. 22(2005), 19-47.
  • Abbassi, M., T., K., Sarih, M., On natural metrics on tangent bundles of Riemannian manifolds, Arch. Math. 41(2005), 71-92.
  • Dida, M., H., Hathout, F., Djaa, M., On the Geometry of the Second Order Tangent Bundle with the Diagonal lift Metric, Int. Journal of Math. Analysis. 3(2009), 443-456.
  • Dombrowski, P., On the Geometry of the Tangent Bundle, J. Reine Angew Math. 210(1962), 73-88.
  • Cheeger, J., Gromoll, D., On the structure of complete manifolds of nonnegative curvature, Ann. of Math, 96(1972), 413-443.
  • García-Río, D., Kupeli, N., Semi-Riemannian Maps and Their Applications, Mathematics and Its Applications, Springer science media, B.V.8 2010.
  • Gezer, A., On the tangent bundle with deformed Sasaki metric, International Electronic Journal of Geometry, 6(2013), 19-31.
  • Gudmundsson, S., Kappos, E., On the Geometry of the Tangent Bundle with the Cheeger-Gromoll metric, Tokyo J. Math. 25(2002), 75-83.
  • Gudmundsson, S., Kappos, E., On the Geometry of the Tangent Bundles, Expo. Math. 20(2002), 1-41.
  • Hathout, F. Dida, H. M., Diagonal lift in the tangent bundle of order two and its applications, Turk. J. Math 30(2006), 373-384.
  • Kowalski, O., Curvature of the induced Riemannian metric of the tangent bundle of a Riemannian manifold, J. Reine Angew.math. 250(1971), 124-129.
  • Musso, E., Tricerri, F., Riemannian metric on tangent bundle, Ann. Math. Pura. Appl. 150(1988), 1-19.
  • O'Neill, B., Semi-Riemannian geometry with applications to relativity, Academic Press, New York, 1983.
  • Oproiu, V., Some new geometric structures on the tangent bundles. Publ Math. Debrecen, 55(1999) 261-281.
  • Oproiu, V., Papaghiuc, N., On the geometry of tangent bundle of a (pseudo-) Riemannian manifold, An Stiint Univ Al I Cuza Iasi Mat 44(1998) 67-83.
  • Sasaki, S., On the differential geometry of tangent bundles of Riemannian manifolds, Tohoku Math. J. 10(1958) 338-358.
  • Sekizawa, M., Curvatures of Tangent Bundles with Cheeger-Gromoll metric, Tokyo J. Math. 14(1991) 407-417.
  • Wang, J., Wang, Y., On the geometry of tangent bundles with the rescaled metric, arXiv:1104.5584v1.
  • Yano, K., Ishihara, S., Tangent and cotangent bundles, Marcel Dekker, Inc., New York 1973.
  • Zayatuev, B. V., On geometry of tangent Hermitian surface, Webs and Quasigroups. T.S.U. (1995) 139-143.
  • Zayatuev, B. V., On some classes of almost-Hermitian structures on the tangent bundle, Webs and Quasigroups. T.S.U. (2002) 103--106.
  • Zhong, H. H., Lei, S., Geometry of tangent bundle with Cheeger--Gromoll type metric, Math. Anal. Appl. 402(2013) 493-504.

On the Geometry of the Tangent Bundle With Vertical Rescaled Metric

Yıl 2019, , 222 - 235, 01.02.2019
https://doi.org/10.31801/cfsuasmas.443735

Öz

Let (M,g) be a n-dimensional smooth Riemannian manifold. In the present paper, we introduce a new class of natural metrics denoted by G^{f} and called the vertical rescaled metric on the tangent bundle TM. We calculate its Levi-Civita connection and Riemannian curvature tensor. We study the geometry of (TM,G^{f}) and several important results are obtained on curvature, Einstein structure, scalar and sectional curvatures

Kaynakça

  • Abbassi, M., T., K., Note on the classification theorems of g-natural metrics on the tangent bundle of a Riemannian manifold (M; g), Comment. Math. Univ. Carolin. 45(2004), 591-596.
  • Abbassi, M., T., K., Sarih, M., On some hereditary properties of Riemannian g-natural metrics on tangent bundles of Riemannian manifolds, Differential Geom. Appl. 22(2005), 19-47.
  • Abbassi, M., T., K., Sarih, M., On natural metrics on tangent bundles of Riemannian manifolds, Arch. Math. 41(2005), 71-92.
  • Dida, M., H., Hathout, F., Djaa, M., On the Geometry of the Second Order Tangent Bundle with the Diagonal lift Metric, Int. Journal of Math. Analysis. 3(2009), 443-456.
  • Dombrowski, P., On the Geometry of the Tangent Bundle, J. Reine Angew Math. 210(1962), 73-88.
  • Cheeger, J., Gromoll, D., On the structure of complete manifolds of nonnegative curvature, Ann. of Math, 96(1972), 413-443.
  • García-Río, D., Kupeli, N., Semi-Riemannian Maps and Their Applications, Mathematics and Its Applications, Springer science media, B.V.8 2010.
  • Gezer, A., On the tangent bundle with deformed Sasaki metric, International Electronic Journal of Geometry, 6(2013), 19-31.
  • Gudmundsson, S., Kappos, E., On the Geometry of the Tangent Bundle with the Cheeger-Gromoll metric, Tokyo J. Math. 25(2002), 75-83.
  • Gudmundsson, S., Kappos, E., On the Geometry of the Tangent Bundles, Expo. Math. 20(2002), 1-41.
  • Hathout, F. Dida, H. M., Diagonal lift in the tangent bundle of order two and its applications, Turk. J. Math 30(2006), 373-384.
  • Kowalski, O., Curvature of the induced Riemannian metric of the tangent bundle of a Riemannian manifold, J. Reine Angew.math. 250(1971), 124-129.
  • Musso, E., Tricerri, F., Riemannian metric on tangent bundle, Ann. Math. Pura. Appl. 150(1988), 1-19.
  • O'Neill, B., Semi-Riemannian geometry with applications to relativity, Academic Press, New York, 1983.
  • Oproiu, V., Some new geometric structures on the tangent bundles. Publ Math. Debrecen, 55(1999) 261-281.
  • Oproiu, V., Papaghiuc, N., On the geometry of tangent bundle of a (pseudo-) Riemannian manifold, An Stiint Univ Al I Cuza Iasi Mat 44(1998) 67-83.
  • Sasaki, S., On the differential geometry of tangent bundles of Riemannian manifolds, Tohoku Math. J. 10(1958) 338-358.
  • Sekizawa, M., Curvatures of Tangent Bundles with Cheeger-Gromoll metric, Tokyo J. Math. 14(1991) 407-417.
  • Wang, J., Wang, Y., On the geometry of tangent bundles with the rescaled metric, arXiv:1104.5584v1.
  • Yano, K., Ishihara, S., Tangent and cotangent bundles, Marcel Dekker, Inc., New York 1973.
  • Zayatuev, B. V., On geometry of tangent Hermitian surface, Webs and Quasigroups. T.S.U. (1995) 139-143.
  • Zayatuev, B. V., On some classes of almost-Hermitian structures on the tangent bundle, Webs and Quasigroups. T.S.U. (2002) 103--106.
  • Zhong, H. H., Lei, S., Geometry of tangent bundle with Cheeger--Gromoll type metric, Math. Anal. Appl. 402(2013) 493-504.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Hamou Mohammed Dida Bu kişi benim

Fouzi Hathout

Abdelhalim Azzouz Bu kişi benim

Yayımlanma Tarihi 1 Şubat 2019
Gönderilme Tarihi 15 Şubat 2017
Kabul Tarihi 6 Aralık 2017
Yayımlandığı Sayı Yıl 2019

Kaynak Göster

APA Dida, H. M., Hathout, F., & Azzouz, A. (2019). On the Geometry of the Tangent Bundle With Vertical Rescaled Metric. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 222-235. https://doi.org/10.31801/cfsuasmas.443735
AMA Dida HM, Hathout F, Azzouz A. On the Geometry of the Tangent Bundle With Vertical Rescaled Metric. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Şubat 2019;68(1):222-235. doi:10.31801/cfsuasmas.443735
Chicago Dida, Hamou Mohammed, Fouzi Hathout, ve Abdelhalim Azzouz. “On the Geometry of the Tangent Bundle With Vertical Rescaled Metric”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, sy. 1 (Şubat 2019): 222-35. https://doi.org/10.31801/cfsuasmas.443735.
EndNote Dida HM, Hathout F, Azzouz A (01 Şubat 2019) On the Geometry of the Tangent Bundle With Vertical Rescaled Metric. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 222–235.
IEEE H. M. Dida, F. Hathout, ve A. Azzouz, “On the Geometry of the Tangent Bundle With Vertical Rescaled Metric”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 68, sy. 1, ss. 222–235, 2019, doi: 10.31801/cfsuasmas.443735.
ISNAD Dida, Hamou Mohammed vd. “On the Geometry of the Tangent Bundle With Vertical Rescaled Metric”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (Şubat 2019), 222-235. https://doi.org/10.31801/cfsuasmas.443735.
JAMA Dida HM, Hathout F, Azzouz A. On the Geometry of the Tangent Bundle With Vertical Rescaled Metric. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:222–235.
MLA Dida, Hamou Mohammed vd. “On the Geometry of the Tangent Bundle With Vertical Rescaled Metric”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 68, sy. 1, 2019, ss. 222-35, doi:10.31801/cfsuasmas.443735.
Vancouver Dida HM, Hathout F, Azzouz A. On the Geometry of the Tangent Bundle With Vertical Rescaled Metric. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):222-35.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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